Electron diffraction is an identification technique for solid crystalline phases, particles, and surfaces observed in a transmission electron microscope (TEM) or other electron diffractometer. It is often used in conjunction with elemental analysis, which is often performed by fluorescence spectrometry (called EDS for energy dispersive spectrometry) on the TEM. Together these techniques are used by scientists to identify the chemical composition and structure of unknown materials of very small size, typically 10""s to 1000""s of nanometers (nm), in the fields of metallurgy, catalysis, analytical chemistry, mineralogy, forensics, and environmental studies.
Identification of a known single crystal phase by electron diffraction takes the form of interpreting a lattice net of spots produced in the diffraction mode of the TEM or electron diffractometer. Images can be recorded by (a) a fluorescent screen and photographic film, or (b) an electronic detector capable of converting diffracted electron impulses in two dimensional space to electronic signals which are converted, with their spacial positions, to digital form and stored in a computer file.
In case (a) the two minimum repeat distances (r1, r2) of the lattice net and their included acute angle (xcfx86) are measured on the film. The corresponding maximum d-spacings, (d1, d2), in Angstrom units (xc3x85) are calculated from each minimum repeat distance and the electron voltage or electron wavelength and the camera length (the distance between sample and recorder) of the diffractometer or TEM by Equation 1 (see below), or in case (b) the electronic file of converted signal impulses and positions (r1, r2), together with the electron voltage or electron wavelength and the camera length of the diffractometer or TEM is processed through computer programs or other calculations to produce the corresponding maximum d-spacings, (d1, d2), in Angstrom units by Equation 1 shown below:
r*d=C*xcexxe2x80x83xe2x80x83(Equation 1)
wherein
r=distance of spot from center in centimeters (also known as r-spacing),
d=d-spacing in Angstroms (1 xc3x85=10xe2x88x9210 meter)
C=camera constant in millimeter-Angstroms,
xcex=electron wavelength in nanometers,
which is determined from the electron voltage by conventional means, using the well known de Broglie Principle and related formulae.
Equation 1 is the well known application of Bragg""s Law to electron diffraction (Reference 1). The two r-spacings (r1, r2) are the shortest and second shortest distances, respectively, to the center of the pattern (the direct beam), whereas the two d-spacings (d1, d2) are the largest and second largest d-spacings, respectively, of the zone of the pattern. The included angle, xcfx86, is both the acute angle between the lattice rows containing r1 and r2, respectively, and the interplanar angle (acute) between the sets of parallel planes whose interplanar spacings are, respectively d1, and d2. These relationships as well as the terms, xe2x80x9cd-spacing,xe2x80x9d xe2x80x9czone,xe2x80x9d xe2x80x9cinterplanar,xe2x80x9d are well known to those skilled in the art of crystallography.
An identification of a previously known material (or phase) is obtained when the values d1, d2, and xcfx86 are matched to measured or calculated values for a known material (References 2, 3).
The values of d1, d2, of known materials are calculated from their unit cells through the well known formula for triclinic unit cells (Reference 4) by varying Miller Indeces (h,k,l) from among those found in FIG. 1. These combinations (h1, k1, l1) and density (and low zone indeces [U,V,W] (FIG. 1.). These zones will also exhibit the highest spot symmetry in their electron diffraction patterns and will therefore be recognizable as the most desirable zones to be measured experimentally. The angle xcfx86 is calculated from the well known formula for tricilinic unit cells (Reference 4).
Candidate materials for a xe2x80x9chitxe2x80x9d are found by matching the values of d1, d2, and xcfx86 determined experimentally to the values calculated from the unit cells of the known materials. Often the solutions above are not unique. In such cases, elemental analysis, for example by fluorescence spectrometry mentioned above, usually decides in favor of one or a very few possible, often chemically or structurally related, phases. Knowledge of sample history or other physical or analytical data might also be required for the final identification.
Prior art of comprehensive databases for electron diffraction is described in References 5, 6, 7, 8, and 9 and is summarized below.
The Powder Diffraction File, or PDF (Reference 6) of the International Centre for Diffraction Data (ICDD) is an x-ray polycrystalline diffraction database of d-spacings and other crystallographic data which is available in computer, microfiche, or book form. Its known disadvantage for use in electron diffraction is that it does not include d-spacings observed by double diffraction, because double diffraction is rare in x-ray diffraction.
Double diffraction is the phenomenon of a diffracted beam being rediffracted before exiting the crystal. The effect of this important phenomenon is that d-spacings which are unobservable (xe2x80x9cextinctxe2x80x9d) by x-radiation appear in the electron diffraction pattern of the same material, as if there were no three-dimensional symmetry elements. These additional d-spacings due to double diffraction, which fill in x-ray extinct values, are included automatically if one calculates electron diffraction patterns from a reduced unit cell. This is the premise of ZONES. In this manner, no extra rings are calculated and none are missed. Further, there are no symmetry considerations.
Even more importantly, the PDF contains no interplanar angles (xcfx86). One might use two d-values as d1 and d2 and calculate the interplanar angle from the Miller indeces (h,k,l) of each, which are usually on the PDF card for each material. This is a slow procedure of limited applicability to single crystal identifications which have very limited possible solutions.
The NIST/ICDD/Sandia Electron Diffraction Database (References 5, 6) is a polycrystalline computer database developed specifically for electron diffraction, incorporating both the PDF and NIST Crystal Data (described below). Since it contains no interplanar angles, it would have to be used for d1 and d2 only, requiring a separate calculation of xcfx86. Since no Miller indeces are included in this database, it would be even more cumbersome to use than the PDF for single crystal electron diffraction.
Another database is available in book form only, the Elemental and Interplanar Spacing Index (EISI), available from ICCD. (References 6, 7) On one line per phase it contains an alphabetical listing of elements (by symbol) and the highest ten d-spacings in decreasing order. However it is a polycrystalline database as are the above databases, and therefore the EISI does not include interplanar angles (xcfx86). Nor does it include the effects of double diffraction. Its use for polycrystalline electron diffraction is discussed in Reference 6. For single crystal electron diffraction it has the same shortcomings as as the preceding databases with respect to interplanar angles.
NIST Crystal Data, currently in Release J of 1997 on CD-ROM, began in the mid-1980""s as a large computer file (first available on tape) of crystallographic and related data obtained from several other original sources: ICDD (then known as The Joint Committee for Powder Diffraction Standardsxe2x80x94JCPDS), The Cambridge Crystallographic Centre (U.K.), The Metals Data Center (Ottawa, Canada), The Inorganic Structural Data Center (Germany), and the open literature. Today, the database contains information on 237,659 organic, inorganic, and organometallic phases (of which 79,136 are inorganic) and is available on CD-ROM from NIST or ICDD (References 5, 6, 8). For each phase (also called a xe2x80x9cknown materialxe2x80x9d, as defined above), the data is organized into sixteen different types of several related fields each (Reference 8). The CD-ROM contains a single flat text file of these types for each phase, plus a coded literature reference file (one of the fields), and various special use files, not used here. There are no d-spacings or any PC software for searching or organizing the data in Release J, 1997, on CD-ROM. However, through its reduced unit cells, this database forms the basis for calculating diffraction patterns in the ZONES database.
In addition, an electron microscopist trained in crystallography might, in favorable circumstances, obtain two zone axis patterns and the interaxial angle between them. NIST has written software to compute the reduced unit cell from this data, which can be searched against the NIST Crystal Data reduced unit cell fields (References 5, 6, 8). This is a powerful and patented (Reference 9) search/match procedure in the hands of a specialist, but it is not as simple as matching three numbers (d1, d2, xcfx86). There is considerable mathematical complexity in determining reduced unit cell parameters from diffraction data by procedures guaranteed to produce the same (xe2x80x9cuniquexe2x80x9d, xe2x80x9cconventionalxe2x80x9d) result (from among all the possible permutations) of a, b, c, and of xcex1, xcex2, xcex3, regardless of which two crystal zone axis patterns are used. It can also be difficult to obtain the required two zone axis patterns and their interaxial angle from the same crystal.
The present invention is directed to a method for creating a searchable database of crystal electron diffraction data comprising: (a) creating tables within a relational database, said tables comprising Code data, Formula data, and Element data; wherein said Code data includes information relating to the d-spacings and acute angles of diffraction patterns of crystals, said Formula data includes information relating to the chemical formulae of said crystals, and said Element data includes information relating to the presence of elements of high atomic number in said crystals; (b) creating at least one macro for performing searches using said tables; said at least one macro including the steps of: (i) requesting input data relating to observed d-spacings, acute angles, experimental error limits, and anticipated atomic numbers of an experimental sample; (ii) comparing said input data with the data in said tables in accordance with said experimental error limits; and (iii) generating at least one report listing the crystals within said tables that match said input data.
The invention is also directed to a method for classifying crystal electron diffraction data obtained from an experimental sample, comprising: (a) generating a relational database comprising: (i) at least three tables holding Code data, Formula. data, and Element data, respectively; wherein said Code data includes information relating to the d-spacings and acute angles of diffraction patterns of crystals, said Formula data includes information relating to the chemical formulae of said crystals, and said Element data includes information relating to the presence of elements of high atomic number in said crystals; (ii) at least one macro for performing searches using said tables; said at least one macro including the steps of: (1) requesting input data relating to observed d-spacings, acute angles, experimental error limits, and anticipated atomic numbers of an experimental sample; (2) comparing said input data with the data in said tables in accordance with said experimental error limits; and (3) generating at least one report listing the crystals within said tables that match said input data; and (b) using said macro of said relational database to enter electron diffraction data obtained from said experimental sample and to obtain said at least one report.
The invention also provides a relational database for classifying crystal electron diffraction data obtained from an experimental sample, said database comprising: (a) at least three tables holding Code data, Formula data, and Element data, respectively; wherein said Code data includes information relating to the d-spacings and acute angles of diffraction patterns of crystals, said Formula data includes information relating to the chemical formulae of said crystals, and said Element data includes information relating to the presence of elements of high atomic number in said crystals; (b) at least one macro for performing searches using said tables; said at least one macro including the steps of: (i) requesting input data relating to observed d-spacings, acute angles, experimental error limits, and anticipated atomic numbers of an experimental sample.; (ii) comparing said input data with the data in said tables in accordance with said experimental error limits; and (iii) generating at least one report listing the crystals within said tables that match said input data.
The present invention provides the construction and searching of a relational database of values d1, d2, and xcfx86, plus coded elemental composition, for known crystalline solids. Through the use of new software and computational methods and procedures associated with this relational database, unknown materials are matched to 79,136 inorganic compounds in embodiment.
The present invention provides the following advantages: (1) it permits an electron microscopist with little or no training in crystallography, and (2) only elementary training in common personal computer (PC) software tools to (3) identify the substance or substances which produced a single crystal electron diffraction pattern from (4) among as wide as possible a set of xe2x80x9cknownsxe2x80x9d. In the present invention, identification of all inorganic materials in the NIST Crystal Data file, in (5) less than 14 seconds search time (the common limit of human patience in such matters)is accomplished.
All of the above five advantages are met with the present invention. Unique features of this invention not found elsewhere are: (1) Rational inclusion in the database of specific d-spacings which produce spots by xe2x80x9cdouble diffractionxe2x80x9d through the use of reduced unit cell parameters; (2) use of a commercially available database management system, in this embodiment, Microsoft ACCESS 97, for producing the relevant crystallographic and elemental parameters and storing these and other phase data in a relational database with database xe2x80x9cobjectsxe2x80x9d such as xe2x80x9ctables,xe2x80x9d xe2x80x9cqueries,xe2x80x9d xe2x80x9cmacros,xe2x80x9d xe2x80x9creports,xe2x80x9d and xe2x80x9cmodulesxe2x80x9d (Visual Basic for Applications code in this embodiment). (3) Use of experimental error limits for d1, d2, and xcfx86 to greatly reduce the number of potential solutions to examine manually in the table, (4) below, and (4) production of an output table and report which can be further customized, sorted, filtered, exported (in common formats), or further reported with common database tools, and (5) ability to customize the search to include other specific information particular to each search problem with common database tools, for example, in this embodiment Microsoft ACCESS 97.
The practice of the invention is accomplished as follows:
1. (a) The values of d1, d2, and xcfx86, along with (b) their error limits as a constant percentage of each d-spacing (d1, d2) and in degrees for xcfx86, and, (c) the element symbols (above atomic number 10 only) for the elements present in the sample (a maximumm of ten), are input to a computer program, ZONES, incorporating a relational database of xe2x80x9cknown materials,xe2x80x9d described herein below. A known material in the present embodiment of this invention described here is an inorganic phase present the National Institute of Standards and Technology Crystal Data file, Version J, 1997, (hereinafter referred to as NIST Crystal Data, or NIST CD, or CDxe2x80x94see References 2, 3, 4).
2. The computer program ZONES produces an output table of xe2x80x9ccandidate materials,xe2x80x9d defined as xe2x80x9cknown materialsxe2x80x9d which match the input requirements of 1.(a) through 1.(c), above. The output table consists of, in one line (or record) per candidate material:
(i) a unique index code (hereinafter called the xe2x80x9cCODExe2x80x9d) with which other information, not in the output, may be obtained from another database or other source,
(ii) a chemical formula (hereinafter called xe2x80x9cFORMULAxe2x80x9d),
(iii) a matching database value of d1 in Angstroms,
(iv) a matching database value of d2 in Angstroms,
(v) a matching database value of xcfx86 in degrees,
3. The xe2x80x9ccomputer program incorporating a relational database of known materialsxe2x80x9d in 1., above, consists of a collection of relational database xe2x80x9cobjects,xe2x80x9d which are: (a) program xe2x80x9cmodules,xe2x80x9d in this embodiment written in Microsoft Visual Basic for Applications (VBA) computer program code, and, (b) xe2x80x9ctablesxe2x80x9d and, (c) xe2x80x9cqueriesxe2x80x9d of the tables and other tables produced by the queries, (d) xe2x80x9cmacrosxe2x80x9d (combinations of database commands, involving tables, queries, modules, and other macros) and, (e) xe2x80x9creports, where xe2x80x9cobjects,xe2x80x9d xe2x80x9cmodules,xe2x80x9d xe2x80x9ctables,xe2x80x9d xe2x80x9cqueries,xe2x80x9d xe2x80x9cmacros,xe2x80x9d and xe2x80x9creportsxe2x80x9d all have the common meanings usually associated with a xe2x80x9crelational database,xe2x80x9d which is in this embodiment of the invention Microsoft ACCESS 97.
4. The CODE in 2. (i) is an index used to retrieve other information on candidate materials, for example through additional relational database tables, queries, macros, and reports.
5. The present embodiment of the xe2x80x9cdatabase of known materialsxe2x80x9d in 1., above, contains: (a) the following tables, wherein each table contains one or more records for each xe2x80x9cknown material,xe2x80x9d with a xe2x80x9crecordxe2x80x9d being one line of the table (the usual definition associated with a relational database table):
(i) Database Table tblIZones2. CODE, and 100*d1 in Angstroms, as an integer, hereinafter referred to as xe2x80x9c100D1; xe2x80x9d 100*d2, in Angstroms, as an integer, hereinafter referred to as xe2x80x9c100D2;xe2x80x9d and 10*xcfx86, in degrees, as an integer, hereinafter referred to as xe2x80x9c10PHI,xe2x80x9d
(ii) Database Table tblIFormulas. CODE and FORMULA,
(iii) Database Table tblIElements. CODE, N(1), N(2), N(3), N(4), N(5), N(6), N(7) where N(1) to N(7) are the sums of numeric element identifiers for elements with atomic numbers 1-15, 16-30, 31-45, 46-60, 61-75, 76-90, 91-105, respectively, and each numeric element identifier is 2 raised to the power: Zxe2x88x9215* (ixe2x88x921), where, i is the index of the sums of numeric element identifiers, N(i), ranging from i=1 to i=7 (above), and Z is the atomic number of each element present, and (b) a macro, macZones, which controls the entire search/match procedure, from input to output, and which contains the following separate steps:
(i) Open Module modInputE2
(ii) Run Code E2( )
(iii) Close Module modInputE2
Element symbols are input
Values of N(i) are calculated according to 5.a (iii).
(iv) Open Query qryELE2
(v) Close Query qryELE2
Table tblIElements is queried for matching values of N(1)-N(7).
A table, tblELE, of CODE and matching N(1)-N(7) values is produced.
(vi) Open Module modERRORS
(vii) Run Code ERRDFile ( )
% errors in (d1 and d2), are input and written to a file.
(viii) Run Code ERRPHIFile ( )
Error in xcfx86 (in degrees) is input and written to a file.
(ix) Close Module modERRORS
(x) Open Query qryZones2
(xi) Close Query qryZones2
Tables tblELE, tblIZones2, and tblIFormulas are queried for materials with matching elements, and values of d1, d2, and xcfx86 within input error limits.
An output table of candidate materials, tblZones2, is produced, consisting of CODE, FORMULA, d1, d2, xcfx86, for each.
(xii) Open Report rptzones
A Report is produced from Table tblZones2.
(xiii) Delete tblELE
Table tblELE is deleted in preparation for the next search.
The 25 zones (per each CODE or known material) of FIG. 1 are reduced in number by symmetry, with redundant combinations of d1, d2, xcfx86, removed before storing the results in a data file as integers 100D1, 100D2, 10PHI in 5. (a) (i), above. This process is repeated for each known material with a reduced unit cell. The resulting datafile of xe2x89xa625 unique combinations of 100D1, 100D2, 10PHI, and associated CODE for each known material, is read into the database as Table tblIZones2.
The database table tblIFormulas in 5. (a) (ii) is produced by reading an external datafile containing records of CODE and FORMULA for each known material into the table.
The database table tblIElements in 5. (a) (iii) is produced by reading a datafile of CODE, N(1), N(2), N(3), N(4), N(5), N(6), N(7) for each known material into the database table. This datafile is produced from the external file in 6. by searching each FORMULA for each of the 105 chemical symbols, assigning appropriate numeric indicators for each element symbol found according to 5. (a) (iii), and totaling these numeric indicators within each atomic number range (1 through 7) as in 5. (a) (iii).
The CODE for each known material is consistent throughout the relational database, so that it is possible to relate it to the elements present, the FORMULA, and all stored values of 100D1, 100D2, and 10PHI in a unique manner. Similarly, in the macro macZones, the CODE for each known material is used consistently throughout all queries, intermediate tables, macros, modules, and reports.
Running a Search/Match
The steps required to run a search/match of a single crystal electron diffraction pattern in ZONES, using the present embodiment of this invention, are:
(1) Open the macro macZones.
(2) In Input box 1: From the keyboard, enter a symbol of an element known to be present (Z greater than 10). Repeat for each element (Z greater than 10) known to be present. No unspecified heavy elements will be allowed in the solution, and all specified elements must be present. This requires a complete x-ray fluorescence (or other comparable elemental) analysis. Enter xe2x80x9c0xe2x80x9d (zero) to stop adding elements. All elements with Zxe2x89xa610 cannot be entered and are considered to be possibly present (i.e., any combination of these light elements, including none, is allowed).
(3) Input box 2a: Enter d1, the largest d-value of the zone, in Angstroms.
(4) Input box 2b: Enter d2, the second largest d-value of the zone, in Angstroms.
(5) Input box 2c: Enter xcfx86, the angle between the repeat distances in the diffraction pattern corresponding to d1 and d2, respectively, in degrees.
(6) Input box 3a: Enter the experimental error limit on d-values in % (recommended input 1.5). A match occurs when a database d-value is within this percent of the experimental value, i.e. when
(100xe2x88x92err. d)*d(exptl.)xe2x89xa6[100D(database, 1 or 2)]xe2x89xa6(100+err. d)*d(exptl.).
(7) Input box 3b: Enter the experimental error limit on xcfx86 in degrees (recommended input 1.0). A match occurs when
10*(xcfx86(exptl.)xe2x88x92err. xcfx86)xe2x89xa6[10PHI(database)]xe2x89xa610*(xcfx86(exptl.)+err. xcfx86).
Table 1. Stored Zones.
Table 2. Fluorite.
Table 3. Zircon.
Table 4. Molybdite.
Table 5. Hornblende, first zone.
Table 6. Hornblende, second zone.
Table 7. Fe3C.
Table 8. Hollandite, first zone.
Table 9. Hollandite, second zone.
Table 10. M2X, first zone, Nb.
Table 11. M2X, second zone, Nb.
Table 12. M2X, first zone, Ni.
Table 13. M2X, second zone, Ni.
Table 14. M6C, Cr, Nb.
Table 15. M6C, Fe, Nb.
Table 16. ZrH2.
Table 17. Search Simulations.